It might work for you but I don't think you'll save as much as you might think. The batteries on the cordless tools are a wear item. And they are not cheap to replace. Price a new battery for the trimmer and see if the deal still looks good.

In general I don't like corded or cordless outdoor tools. They can be useful but for all around use, I prefer something with more power. That said, my neighbor maintains hi yard with a corded trimmer and I can't tell the difference :). I can definitely do more with my gas trimmer like shred my leaf bins and use mine as a brushcutter. I also have to work to maintain the small engine. His is a throwaway and gets done what he needs to get done. Can't argue with that.

Put my vote for the cordless line trimmer. The advantages outweigh the battery cost to many people. Hopefully someone will chime in on their 24 v battery life was/ costs etc. Clean, always start, always run, quiet. Hang 'em on the wall charger when done and you are ready to go. Generally have good power for edge trimming, but as masiman said- the extra power of gas lets you do extra tasks. Many shops have quit working on basic trimmers- gas or otherwise due to the cost effectiveness of the repair- at least on the customer pay side of things. I too have a brush cutter but very litle trimming gets done by me in the yard anyways. I think my other half threw the electric over the fence tho....